Trees are made up by given communication routes. The communication routes comprise many nodes. The tree is formed as a set of branches connected with the many nodes. A problem that the plural routes connected with the plural ingress nodes is given to a certain egress node and the number of the trees is minimized is solved by means of the mixed-integer program. The mixed-integer program gives the optimum solution certainly.
When the scale of the problem becomes large and the numbers of the given routes and the given trees become large, it is inevitable that a time necessary for deriving the optimum solution becomes extremely long. Accordingly, it is desirable to quickly derive an approximate solution which keeps down the number of the trees, even if the optimum solution is not necessarily obtained and the number of the trees is not minimized.